One-loop factorization for inclusive hadron production in p-A collisions in the saturation formalism

Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x: Complete NLO Results and Predictions

We compute the back-to-back dijet cross section in deep inelastic scattering at small x to next-to-leading order (NLO) in the color glass condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse-momentum-dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum P_{⊥} of the dijet pair to the dijet momentum imbalance q_{⊥}; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in x that is kinematically constrained to satisfy both the lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.

Harmonics of Parton Saturation in Lepton-Jet Correlations at the Electron-Ion Collider

Parton saturation is one of the most intriguing phenomena in the high energy nuclear physics research frontier, especially in the upcoming era of the Electron-Ion Collider (EIC). The lepton-jet correlation in deep inelastic scattering provides us with a new gateway to the parton saturation at the EIC. In particular, we demonstrate that azimuthal angle anisotropies of the lepton-jet correlation are sensitive to the strength of the saturation momentum in the EIC kinematic region. In contrast to the predictions based on the collinear framework calculation, significant nuclear modification of the anisotropies is observed when we compare the saturation physics results in e+p and e+Au scatterings. By measuring these harmonic coefficients at the EIC, one can conduct quantitative analyses in different collisional systems and unveil compelling evidence for saturation effects.

Pursuing the Precision Study for Color Glass Condensate in Forward Hadron Productions

With the tremendous accomplishments of RHIC and the LHC experiments and the advent of the future electron-ion collider on the horizon, the quest for compelling evidence of the color glass condensate (CGC) has become one of the most aspiring goals in the high energy quantum chromodynamics research. Pursuing this question requires developing the precision test of the CGC formalism. By systematically implementing the threshold resummation, we significantly improve the stability of the next-to-leading-order calculation in CGC for forward rapidity hadron productions in pp and pA collisions, especially in the high p_{T} region, and obtain reliable descriptions of all existing data measured at RHIC and the LHC across all p_{T} regions. Consequently, this technique can pave the way for the precision studies of the CGC next-to-leading-order predictions by confronting them with a large amount of precise data.

Mining for Gluon Saturation at Colliders

Quantum chromodynamics (QCD) is the theory of strong interactions of quarks and gluons collectively called partons, the basic constituents of all nuclear matter. Its non-abelian character manifests in nature in the form of two remarkable properties: color confinement and asymptotic freedom. At high energies, perturbation theory can result in the growth and dominance of very gluon densities at small-x. If left uncontrolled, this growth can result in gluons eternally growing violating a number of mathematical bounds. The resolution to this problem lies by balancing gluon emissions by recombinating gluons at high energies: phenomena of gluon saturation. High energy nuclear and particle physics experiments have spent the past decades quantifying the structure of protons and nuclei in terms of their fundamental constituents confirming predicted extraordinary behavior of matter at extreme density and pressure conditions. In the process they have also measured seemingly unexpected phenomena. We will give a state of the art review of the underlying theoretical and experimental tools and measurements pertinent to gluon saturation physics. We will argue for the need of high energy electron-proton/ion colliders such as the proposed EIC (USA) and LHeC (Europe) to consolidate our knowledge of QCD knowledge in the small x kinematic domains.

Quenching of Light Hadron Spectra in p-A Collisions from Fully Coherent Energy Loss

We single out the role of fully coherent induced gluon radiation on light hadron production in p-A collisions. The effect has an interesting color structure, as the induced radiation depends on the global color charge of the partonic subprocess final state. Baseline predictions for light hadron nuclear suppression in p-Pb collisions at the LHC are provided, taking into account only the effect of fully coherent energy loss, which proves of the same order of magnitude as gluon shadowing or saturation. This underlines the need to include fully coherent energy loss in phenomenological studies of hadron production in p-A collisions.

Elliptic Flow of Heavy Quarkonia in pA Collisions

Using the dilute-dense factorization in the color glass condensate framework, we investigate the azimuthal angular correlation between a heavy quarkonium and a charged light hadron in proton-nucleus collisions. We extract the second harmonic v_{2}, commonly known as the elliptic flow, with the light hadron as the reference. This particular azimuthal angular correlation between a heavy meson and a light hadron was first measured at the LHC recently. The experimental results indicate that the elliptic flows for heavy flavor mesons (J/ψ and D^{0}) are almost as large as those for light hadrons. Our calculation demonstrates that this result can be naturally interpreted as an initial state effect due to the interaction between the incoming partons from the proton and the dense gluons inside the target nucleus. Since the heavy quarkonium v_{2} exhibits a weak mass dependence according to our calculation, we predict that the heavy quarkonium ϒ should have a similar elliptic flow as compared to that of the J/ψ, which can be tested in future measurements.

Forward particle production in proton-nucleus collisions at next-to-leading order

We consider the next-to-leading order (NLO) calculation of single inclusive particle production at forward rapidities in proton-nucleus collisions and in the framework of the Color Glass Condensate (CGC). We focus on the quark channel and the corrections associated with the impact factor. In the first step of the evolution the kinematics of the emitted gluon is kept exactly (and not in the eikonal approximation), but such a treatment which includes NLO corrections is not explicitly separated from the high energy evolution. Thus, in this newly established “factorization scheme”, there is no “rapidity subtraction”. The latter suffers from fine tuning issues and eventually leads to an unphysical (negative) cross section. On the contrary, our reorganization of the perturbation theory leads by definition to a well-defined cross section and the numerical evaluation of the NLO correction is shown to have the correct size.

Next-to-Leading Order Computation of Exclusive Diffractive Light Vector Meson Production in a Saturation Framework

We perform the first next-to-leading order computation of the γ^{(*)}→V (ρ,ϕ,ω) exclusive impact factor in the QCD shock-wave approach and in the most general kinematics. This paves the way to the very first quantitative study of high-energy nucleon and nucleus saturation beyond the leading order for a whole range of small-x exclusive processes, to be measured in ep, eA, pp, and pA collisions at existing and future colliders.

Next-to-leading-order forward hadron production in the small-x regime: the role of rapidity factorization

Single inclusive hadron production at forward rapidity in high energy p+A collisions is an important probe of the high gluon density regime of QCD and the associated small-x formalism. We revisit an earlier one-loop calculation to illustrate the significance of the "rapidity factorization" approach in this regime. Such factorization separates the very small-x unintegrated gluon density evolution and leads to a new correction term to the physical cross section at one-loop level. Importantly, this rapidity factorization formalism remedies the previous unphysical negative next-to-leading-order contribution to the cross section. It is much more stable with respect to "rapidity" variation when compared to the leading-order calculation and provides improved agreement between theory and experiment in the forward rapidity region.

Towards the test of saturation physics beyond leading logarithm

We present results from the first next-to-leading-order (NLO) numerical analysis of forward hadron production in pA and dA collisions in the small-x saturation formalism. Using parton distributions and fragmentation functions at NLO, as well as the dipole amplitude from the solution to the Balitsky-Kovchegov equation with running coupling, together with the NLO corrections to the hard coefficients, we obtain a good description of the available RHIC data in dAu collisions. In the large p⊥ region beyond the saturation scale, we find that the NLO correction becomes dominant and negative, which indicates that other physics beyond NLO becomes important and should also be taken into account. Furthermore, we make predictions for forward hadron production in pPb collisions at the LHC. This analysis not only incorporates the important NLO corrections for all partonic channels, but also reduces the renormalization scale dependence and helps to significantly reduce the theoretical uncertainties. It therefore provides a precise test of saturation physics beyond the leading logarithmic approximation.

Sudakov resummation in the small-x saturation formalism

Through an explicit calculation of massive scalar particle (e.g., Higgs boson) production in high energy pA collisions up to one-loop order, we demonstrate, for the first time, that the Sudakov-type logarithms in hard processes in the small-x saturation formalism can be systematically separated from the small-x logarithms. The generic feature of the Sudakov logarithms and all order resummation is derived. This calculation shall provide us deep insights into the understanding of factorizations in the saturation formalism. We further comment on the phenomenological implications in the LHC energy regime and extension to other hard processes in small-x calculations.